Abstract: Suppose , are sets of real numbers, is a collection of vectors in , having nonzero coordinates all from and satisfying for . Theorem 1.1 establishes a polynomial upper bound for , generalizing previous results for subsets of a set and -vectors. Theorem 1.4 asserts that if then . For , , Theorem 1.5 gives , where equality holds if and only if is a "signed" Steiner-system.